derivative of (x^2-2x-3/((x-1)^2))

解答

\frac{d}{d x} (\frac{x ^{2} - 2 x - 3}{( x - 1 ) ^{2}})

\frac{8}{( x - 1 ) ^{3}}

求解步骤

\frac{d}{d x} (\frac{x ^{2} - 2 x - 3}{( x - 1 ) ^{2}})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{2} - 2 x - 3 ) ( x - 1 ) ^{2} - \frac{d}{d x} ( ( x - 1 ) ^{2} ) ( x ^{2} - 2 x - 3 )}{( ( x - 1 ) ^{2} ) ^{2}}

\frac{d}{d x} (x^{2} - 2 x - 3) = 2 x - 2

\frac{d}{d x} ((x - 1)^{2}) = 2 (x - 1)

= \frac{( 2 x - 2 ) ( x - 1 ) ^{2} - 2 ( x - 1 ) ( x ^{2} - 2 x - 3 )}{( ( x - 1 ) ^{2} ) ^{2}}

化简

\frac{( 2 x - 2 ) ( x - 1 ) ^{2} - 2 ( x - 1 ) ( x ^{2} - 2 x - 3 )}{( ( x - 1 ) ^{2} ) ^{2}} : \frac{8}{( x - 1 ) ^{3}}

= \frac{8}{( x - 1 ) ^{3}}

n = 2 \sum \infty \frac{9}{n ( n + 2 )}

\frac{d}{d x} (\frac{x}{1 + x ^{2} + x ^{4}})

\frac{d}{d x} (- 7 x^{3} - \frac{2}{x ^{3}} + 7 x)

\int \frac{1}{25 x ^{2} - 81} d x

y^{^{'}} - y^{2} = 0